×

zbMATH — the first resource for mathematics

On the existence and nonexistence of Lagrange multipliers in Banach spaces. (English) Zbl 0309.49010

MSC:
49M99 Numerical methods in optimal control
49J27 Existence theories for problems in abstract spaces
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
46E15 Banach spaces of continuous, differentiable or analytic functions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arrow, K. J., Hurwicz, L., andUzawa, H.,Studies in Linear and Nonlinear Programming, Stanford University Press, Stanford, California, 1958. · Zbl 0091.16002
[2] Bazaraa, M. S., andGoode, J. J.,Necessary Optimality Criteria in Mathematical Programming in Normed Linear Spaces, Journal of Optimization Theory and Applications, Vol. 11, No. 3, 1973. · Zbl 0241.90056
[3] Craven, B. D.,Nonlinear Programming in Locally Convex Spaces, Journal of Optimization Theory and Applications, Vol. 10, No. 4, 1972. · Zbl 0229.90041
[4] Makowski, K.,Method of Lagrange Functionals and its Application to Optimization of Dynamic Processes, Polish Academy of Sciences, Warsaw, Poland, Institute of Automatic Control, PhD Thesis, 1966.
[5] Nagahisa, Y., andSakawa, Y.,Nonlinear Programming in Banach Spaces, Journal of Optimization Theory and Applications, Vol. 4, No. 3, 1969. · Zbl 0169.51304
[6] Ritter, K.,Optimization Theory in Linear Spaces, Part III, Mathematische Annalen, Vol. 184, pp. 133-154, 1970. · Zbl 0186.18203 · doi:10.1007/BF01350314
[7] Girsanov, I. V.,Lectures on Mathematical Theory of Extremal Problems, Springer-Verlag, Berlin, Germany, 1972. · Zbl 0234.49016
[8] Findeisen, W., Szymanowski, J., andWierzbicki, A.,Computational Methods in Optimization, Part III (in Polish), WNT, Warsaw, Poland (to appear).
[9] Kelley, J.,General Topology, Van Nostrand, New York, New York, 1964.
[10] Yosida, K.,Functional Analysis, Springer-Verlag, Berlin, Germany, 1966. · Zbl 0152.32102
[11] Day, M.,Normed Linear Spaces, Springer-Verlag, Berlin, Germany, 1973. · Zbl 0268.46013
[12] Varaiya, P. P.,Nonlinear Programming in Banach Spaces, SIAM Journal on Applied Mathematics, Vol. 15, pp. 285-293, 1967. · Zbl 0171.18004
[13] Dunford, N., andSchwartz, J.,Linear Operators, Part 1, John Wiley and Sons (Interscience Publishers), New York, New York, 1958. · Zbl 0088.32102
[14] Lyusternik, L., andSobolev, V.,Elements of Functional Analysis (in Russian), Moscow, USSR, 1965. · Zbl 0141.11601
[15] Luenberger, D.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969. · Zbl 0176.12701
[16] Rolewicz, S.,Functional Analysis and Control Theory (in Polish), WNT, Warsaw, Poland, 1974. · Zbl 0333.49001
[17] Wojtaszczyk, P.,A Theorem on Convex Sets Related to the Abstract Pontryagin Maximum Principle, Bulletin de l’Academie Polonaise des Sciences, Vol. 21, pp. 93-94, 1973.
[18] Kurcyusz, S.,Necessary Optimality Conditions for Problems with Function Space Constraints (in Polish), Technical University of Warsaw, Warsaw, Poland, PhD Thesis, 1974. · Zbl 0296.90050
[19] Weatherwax, R.,General Lagrange Multiplier Theorem, Journal of Optimization Theory and Applications, Vol. 14, No. 7, 1974. · Zbl 0265.49017
[20] Mangasarian, O. L., andFromovitz, S.,The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 37-47, 1967. · Zbl 0149.16701 · doi:10.1016/0022-247X(67)90163-1
[21] Kurcyusz, S.,A Local Maximum Principle for Operator Constraints and its Application to Systems with Time Lags, Control and Cybernetics, Vol. 1, Nos. 1/2, 1973. · Zbl 0331.49018
[22] Banks, H. T., andManitius, A.,Application of Abstract Variational Theory to Hereditary Systems?A Survey, University of Minnesota, Institute of Technology, Technical Report No. 73-11, 1973.
[23] Przy?uski, K. M.,Application of the Shifted Penalty Functional Method to Dynamical Optimization of Delay Systems (in Polish), Technical University of Warsaw, Warsaw, Poland, Institute of Automatic Control, Thesis, 1974.
[24] Kurcyusz, S., andOlbrot, A. W., On the Closure in W 1 q of the Attainable Subspace of Linear Time Lag Systems, Journal of Differential Equations (to appear). · Zbl 0307.93022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.